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Abstract
Background
Due to the advantageous depth dose profile of carbon ion beams, carbon ion therapy is commonly applied in the form of intensity modulated particle therapy (IMPT) with few treatment fields. Carbon ion arc therapy (C-Arc) has recently been proposed to improve dose conformity and increase the dose-averaged linear energy transfer (LETd) inside the target to levels relevant for overcoming tumor radioresistance. In this work, we investigate different energy selection approaches for C-Arc, including a novel greedy energy layer refinement strategy.

Methods
Robust biologically optimized C-Arc plans were generated for six head &neck cancer patient previously treated at the Shanghai Proton and Heavy Ion Center (SPHIC). Different heuristic approaches for mono- and dual-energy C-Arc were implemented, and compared to carbon IMPT pans. A novel greedy energy layer refinement was developed, acting directly on the dose influence matrix, rather than on an iterative plan optimization. A key challenge in C-Arc with few energy layers per angle is the sharpness of the carbon ion Bragg peak, which is challenging for plan robustness. To improve robustness and plan quality, we propose the use of a 6 mm ripple filter instead of the typical 3 mm ripple filter used for carbon IMPT.

Results
Most mono-energetic C-Arc plans were able to meet the established clinical goals, but some of the heuristic energy selection schemes were not universally applicable with low plan quality in some patients. The developed energy layer refinement strategy delivered high quality plans even for complex cases. Mono-energetic C-Arc plans presented an average increase between 10% and 33% in the maximum LETd in the target, with similar or up to 19% improved average target LETd$$_{50\%}$$



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compared to the IMPT carbon ion plans. C-Arc plans with 2 energies per treatment angle, for the employed energy selection heuristic, improved dosimetric quality compared to mono-energetic C-Arc plans, but did not provide the same natural improvement in LETd compared to IMPT.

Conclusions
For small, centrally located targets C-Arc demonstrates the greatest potential, but feasible plans could also be achieved for more complex cases in this work. Further development is necessary for improving C-Arc delivery efficiency and plan quality toward possible clinical application.

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